few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.

Add and subtract within 20.

Analyze patterns and relationships.

Work with radicals and integer exponents.

Understand the connections between proportional relationships, lines, and linear equations.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Work with equal groups of objects to gain foundations for multiplication.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Represent and solve problems involving addition and subtraction.

Use the four operations with whole numbers to solve problems.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

Represent and analyze quantitative relationships between dependent and independent variables.

Rewrite rational expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand properties of multiplication and the relationship between multiplication and division.

Understand the relationship between zeros and factors of polynomials.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Understand solving equations as a process of reasoning and explain the reasoning.

Use properties of operations to generate equivalent expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Gain familiarity with factors and multiples.
problem_activity: Task
The students in Mr. Sanchez's class are converting distances measured in miles to kilometers. To estimate the number of kilometers, Abby takes the number of miles, doubles it, then subtracts 20% of the result. Renato ﬁrst divides the number of miles by 5, then multiplies the result by 8.
Write an algebraic expression for each method.
Use your answer to part (a) to decide if the two methods give the same answer.


correct_option_index: 28